Polarized triple-collinear splitting functions at NLO for processes with photons

We compute the polarized splitting functions in the triple collinear limit at next-to-leading order accuracy (NLO) in the strong coupling alpha(S), for the splitting processes gamma -> qq gamma, gamma -> qqg and g -> qq gamma. The divergent structure of each splitting function was compared to the predicted behaviour according to Catani's formula. The results obtained in this paper are compatible with the unpolarized splitting functions computed in a previous article. Explicit results for NLO corrections are presented in the context of conventional dimensional regularization (CDR)

To dd, or not to dd: Recent developments and comparisons of regularization schemes

We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them.Comment: 61 pages, 12 figures; version sent to EPJC, references update

A stroll through the loop-tree duality

The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over a Euclidean space. In this article, we review the last developments concerning this framework, focusing on the manifestly causal representation of multi-loop Feynman integrals and scattering amplitudes, and the definition of dual local counter-terms to cancel infrared singularities

Triple collinear splitting functions at NLO for scattering processes with photons

We present splitting functions in the triple collinear limit at next-to-leading order. The computation was performed in the context of massless QCD+QED, considering only processes which include at least one photon. Through the comparison of the IR divergent structure of splitting amplitudes with the expected known behavior, we were able to check our results. Besides that we implemented some consistency checks based on symmetry arguments and cross-checked the results among them. Studying photon-started processes, we obtained very compact results

To d , or not to d : recent developments and comparisons of regularization schemes

We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them

May the four be with you: novel IR-subtraction methods to tackle NNLO calculations

In this manuscript, we summarise all discussions originated as a result of the WorkStop/ThinkStart 3.0: paving the way to alternative NNLO strategies that took place on 4.-6. November 2019 at the Galileo Galilei Institute for Theoretical Physics (GGI). We gratefully acknowledge the support of GGI and the COST Action CA16201 PARTICLEFACE. We wish to thank toW.M. Marroquin and M. Morandini for their help in organising the workshop. P. Banerjee acknowledges support by the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 701647. A.L. Cherchiglia, B. Hiller and M.Sampaio acknowledge support from Fundacao para a Ciencia e Tecnologia (FCT) through the projects UID/FIS/04564/2020 and CERN/FIS-COM/0035/2019. The work of L. Cieri has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 754496. The work of F. Driencourt-Mangin, G. Rodrigo, G. Sborlini and W.J. Torres Bobadilla is supported by the Spanish Government (Agencia Estatal de Investigacion), ERDF funds from European Commission (Grant No. FPA2017-84445-P), Generalitat Valenciana (Grant No. PROMETEO/2017/053) and from the SpanishGovernment (FJCI-2017-32128). T. Engel acknowledges support by the Swiss National Science Foundation (SNF) under contract 200021_178967. C. Gnendiger, R. Pittau, A. Signer and D. Stockinger wish to thank B. Page for his help in establishing (2.60). The work of R. J. Hernandez-Pinto is supported by CONACyT through the Project No. A1-S-33202 (Ciencia Basica) and Sistema Nacional de Investigadores. G. Pelliccioli was supported by the Bundesministerium fur Bildung und Forschung (BMBF, German Federal Ministry for Education and Research) under contract no. 05H18WWCA1. J. Pires was supported by Fundacao para a Ciencia e Tecnologia (FCT, Portugal) through the contract UIDP/50007/2020 and project CERN/FIS-PAR/0024/2019. The work of R. Pittau has been supported by the SpanishGovernment grant PID2019-106087GB-C21 and by the Junta de Andalucia project P18-FR-4314 (fondos FEDER). M. Sampaio acknowledges a research grant from CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico 303482/2017-6). C. Signorile-Signorile was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Grant no. 396021762 - TRR 257.In this manuscript, we report the outcome of the topical workshop: paving the way to alternative NNLO strategies (https://indico.ific.uv.es/e/WorkStop-ThinkStart_3.0), by presenting a discussion about different frameworks to perform precise higher-order computations for high-energy physics. These approaches implement novel strategies to deal with infrared and ultraviolet singularities in quantum field theories. A special emphasis is devoted to the local cancellation of these singularities, which can enhance the efficiency of computations and lead to discover novel mathematical properties in quantum field theories.European Commission 701647Portuguese Foundation for Science and Technology European Commission UID/FIS/04564/2020 CERN/FIS-COM/0035/2019European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant 754496Spanish Government (Agencia Estatal de Investigacion)ERDF funds from European Commission FPA2017-84445-PGeneralitat Valenciana European Commission PROMETEO/2017/053Spanish Government European Commission FJCI-2017-32128 PID2019-106087GB-C21Swiss National Science Foundation (SNSF) 200021_178967Consejo Nacional de Ciencia y Tecnologia (CONACyT) A1-S-33202Sistema Nacional de InvestigadoresFederal Ministry of Education & Research (BMBF) 05H18WWCA1Portuguese Foundation for Science and Technology UIDP/50007/2020 CERN/FIS-PAR/0024/2019Junta de Andalucia P18-FR-4314Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ) 303482/2017-6German Research Foundation (DFG) 396021762 - TRR 257GGIEuropean Cooperation in Science and Technology (COST) CA16201 PARTICLEFAC

On the singular behaviour of scattering amplitudes in quantum field theory

We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop-tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences